Simplify ​( ​17+94 ​)(mod7 ​)

Answer 1

Modulo Method

First need to divide the Dividend by the Divisor:

111

7

= 15.86

Next we take the Whole part of the Quotient (15) and multiply that by the Divisor (7):

15 x 7 = 105

And finally, we take the answer in the second step and subtract it from the Dividend to get the answer to 111 mod 7:

111 - 105 = 6

As you can see, the answer to 111 mod 7 is 6.

Modulus Method

The modulus method requires us to first find out what the highest common multiple of the Divisor (7) is that is equal to or less than the Dividend (111).

We can see that multiples of 7 are 0, 7, 14, 21, etc. The highest multiple that is less than or equal to 111 is 105.

So the final step in the modulus method here is to subtract the divisor highest multiple from the Dividend and answer the question "what is 111 modulus 7?":

111 - 105 = 6

As we can see, this is the same answer as the modulo method and the answer is 6